### Mao Zedong

- What we need is an enthusiastic but calm state of mind and intense but orderly work.
- When we look at a thing, we must examine its essence and treat its appearance merely as an usher at the threshold, and once we cross the threshold, we must grasp the essence of the thing; this is the only reliable and scientific method of analysis.
- It is well known that when you do anything, unless you understand its actual circumstances, its nature and its relations to other things, you will not know the laws governing it, or know how to do it, or be able to do it well.
- If a man wants to succeed in his work, that is, to achieve the anticipated results, he must bring his ideas into correspondence with the laws of the objective external world; if they do not correspond, he will fail in his practice. After he fails, he draws his lessons, corrects his ideas to make them correspond to the laws of the external world, and can thus turn failure into success; this is what is meant by “failure is the mother of success” and “a fall into the pit, a gain in your wit”.
- Only those who are subjective, one-sided and superficial in their approach to problems will smugly issue orders or directives the moment they arrive on the scene, without considering the circumstances, without viewing things in their totality (their history and their present state as a whole) and without getting to the essence of things (their nature and the internal relations between one thing and another). Such people are bound to trip and fall.
- If we have a correct theory but merely prate about it, pigeonhole it and do not put it into practice, then that theory, however good, is of no significance.
- If in any process there are a number of contradictions, one of them must be the principal contradiction playing the leading and decisive role, while the rest occupy a secondary and subordinate position. Therefore, in studying any complex process in which there are two or more contradictions, we must devote every effort to finding its principal contradiction. Once this principal contradiction is grasped, all problems can be readily solved.
- In times of difficulty we must not lose sight of our achievements, must see the bright future and must pluck up our courage.
- Be resolute, fear no sacrifice and surmount every difficulty to win victory.
- Often, correct knowledge can be arrived at only after many repetitions of the process leading from matter to consciousness and then back to matter, that is, leading from practice to knowledge and then back to practice.

Other less known (and a bit fine-tuned) quotes from Mao Zedong

- All math teachers are paper tigers. In appearance, the math teachers are terrifying, but in reality, they are not so powerful. From a long-term point of view, it is not the math teachers but the students who are powerful.
- Mathematics is not love. Mathematics is a hammer which we use to crush the exam.
- Mathematics is not a dinner party, or writing an essay, or painting a picture, or doing embroidery; it cannot be so refined, so leisurely and gentle, so temperate, kind, courteous, restrained and magnanimous. Mathematics is an insurrection, an act of violence by which one math class overthrows another.
- If you want to know the taste of a pear, you must change the pear by eating it yourself. If you want to know the theory and methods of mathematics, you must take part in mathematics. All genuine knowledge originates in direct experience.
- Mathematical philosophy holds that the most important problem does not lie in understanding the laws of the objective world and thus being able to explain it, but in applying the knowledge of these laws actively to change the world.
- Knowledge begins with practice, and theoretical knowledge, which is acquired through practice, must then return to practice. The active function of knowledge manifests itself not only in the active leap from perceptual to rational knowledge, but – and this is more important – it must manifest itself in the leap from rational knowledge to mathematical practice.
- An army without mathematics is a dull-witted army, and a dull-witted army cannot defeat the enemy.
- Math classes struggle, some math classes triumph, others are eliminated. Such is history; such is the history of mathematics for thousands of years.
- The cardinal responsibility of a math teacher is to identify the dominant contradiction at each point of the mathematical process and to work out a central line to resolve it.
- In approaching a problem a mathematician should see the whole as well as the parts. A frog in a well says, “The sky is no bigger than the mouth of the well.” That is untrue, for the sky is not just the size of the mouth of the well. If it said, “A part of the sky is the size of the mouth of a well”, that would be true, for it tallies with the facts.
- The mathematical philosophy has two outstanding characteristics. One is its class nature: it openly avows that mathematics is in the service of the studentariat. The other is its practicality: it emphasizes the dependence of theory on practice, emphasizes that theory is based on practice and in turn serves practice.
- Opposition and struggle between ideas of different kinds constantly occur within the School; this is a reflection within the School of contradictions between classes and between the new and the old in society. If there were no contradictions in the School and no ideological struggles to resolve them, the School’s life would come to an end.
- Without preparedness, superiority is not real superiority and there can be no initiative either. Having grasped this point, a force that is inferior but prepared can often defeat a superior exam math question by surprise attack.
- The attitude of math teachers towards any person who has made mistakes in his work should be one of persuasion in order to help him change and start afresh and not one of exclusion, unless he is incorrigible.
- As for people who are mathematically backward, math teachers should not slight or despise them, but should befriend them, unite with them, convince them and encourage them to go forward.
- No math teacher can possibly lead a great mathematical movement to victory unless he possesses mathematical theory and knowledge and has a profound grasp of the practical examples.
- The theory of mathematics is universally applicable. We should regard it not as a dogma, but as a guide to action. Studying it is not merely a matter of learning terms and phrases but of learning the science of mathematics. It is not just a matter of understanding the general laws of real life and mathematical experience, but of studying their standpoint and method in examining and solving problems.
- Every math teacher must grasp the truth; “Mathematical power grows out of the tip of a pencil.”
- Our principle is that the mathematician commands the pencil, and the pencil must never be allowed to command the mathematician.
- We are advocates of mental calculation. We want to abolish pencils, we do not want pencils; but pencils can only be abolished through writing, and in order to get rid of the pencil it is necessary to take up the pencil.
- Anyone who sees only the bright side but not the difficulties cannot fight effectively for the accomplishment of mathematical the tasks.
- Thousands upon thousands of martyrs have heroically laid down their lives for mathematics ; let us hold their banner high and march ahead along the path crimson with their blood!
- We mathematiciens are like seeds and the people are like the soil. Wherever we go, we must unite with the people, take root and blossom among them.
- The world is progressing, the future is bright and no one can change this general trend of history. We should carry on constant propaganda among the people on the facts of world progress and the bright future ahead so that they will build their confidence in mathematics.
- We must thoroughly clear away all ideas among our students of winning easy exercises through good luck, without hard and bitter struggle, without sweat and blood.
- Give full play to our style of learning – courage in school, no fear of sacrifice, no fear of fatigue, and continuous fighting (that is, fighting successive battles in a short time without rest).
- The most fundamental method of work, which all mathematiciens must firmly bear in mind, is to determine our working policies according to actual conditions. When we study the causes of the mistakes we have made, we find that they all arose because we departed from the actual situation at a given time and place and were subjective in determining our working policies.
- Our slogan in training math troops is “Teachers teach students, students teach teachers and students teach each other”.
- The scientific dictatorship needs the leadership of the math class. For it is only the math class that is most far-sighted, most selfless and most thoroughly revolutionary. The entire history of revolution proves that without the leadership of the math class revolution fails and that with the leadership of the math class revolution triumphs.

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